Number S is obtained by squaring the sum of digits of a two digit numb

Question

Number S is obtained by squaring the sum of the digits of a positive two-digit integer D. If S - D is 27, then the two digit number D is:

A. 24
B. 25
C. 34
D. 45
E. 54

PamPsi10 · Answer

Number S is obtained by squaring the sum of the digits of a positive two-digit integer D. If S - D is 27, then the two digit number D is:

A. 24
B. 25
C. 34
D. 45
E. 54

I'm not certain if I am right but this is how I tackled this question.

I used back solving by testing out the numbers. Let's start with A.

A -> S = (2) + (4) all ^2 -> 6^2 =36. D = 24. 36 - 24 does not equal 27
B -> S = (2) + (5) all ^2 -> 7^2 =49. D = 25. 49 - 25 does not equal 27
C -> S = (3) + (4) all ^2 -> 7^2 =49. D = 34. 49 - 34 does not equal 27
D -> S = (4) + (5) all ^2 -> 9^2 =81. D = 45. 81 - 45 does not equal 27
E -> S = (5) + (4) all ^2 -> 9^2 =81. D = 54. 81 - 54 DOES equal 27

Therefore, E is the correct answer

rajatchopra1994 · Answer

Explanation:

Check by option:
Option E: 54; S = (5+4)^2 = 81
S-D = 81-27 =54

IMO-E

ScottTargetTestPrep · Answer

Letting t = the tens digit of D and u = the units digit of D, we have D = 10t + u and S = (t + u)^2. Since S - D = 27, we can create the equation:

(t + u)^2 - (10t + u) = 27

Since 10t + u is positive, we see that t + u should be at least 6.

If t + u = 6, then (t + u)^2 = 36 and 10t + u (or D) should be 9. However, D is a two-digit number, so t + u actually should be at least 7.

If t + u = 7, then (t + u)^2 = 49 and 10t + u (or D) should be 22. However, 22 is not one of the given choices.

If t + u = 8, then (t + u)^2 = 64 and 10t + u (or D) should be 37. However, 37 is not one of the given choices.

If t + u = 9, then (t + u)^2 = 81 and 10t + u (or D) should be 54. We see that E is the correct answer.

(Note: If you don’t know how to analyze the problem algebraically, you can just check each given answer. For example, take 24, the first given choice. If D = 24, then S = (2 + 4)^2 = 36 and S - D would be 36 - 24 = 12. However, that is not 27. So you can move on to the next given choice and so on, and when you arrive at the last choice, you will see that if D = 54, then S = (5 + 4)^2 = 81 and S - D = 81 - 54 = 27.)

Answer: E

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Number S is obtained by squaring the sum of digits of a two digit numb

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Number S is obtained by squaring the sum of digits of a two digit numb

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